We begin our investigation using approximation (REF ). In
figure REF  we present the time behavior of the VAFs calculated at
two different parameters \(\Gamma _2\)  whereas \(\Gamma _1\)  is chosen
to be fixed. It could be said (see the left-hand panel of figure REF ) that
at small values of \(\Gamma _2\) , the VAF shows a solid-like
[1]} behaviour since there are well defined oscillations
in the whole time domain, which decay as \(a t^{-3/2}\)  at long
times, as it is shown by the dashed line. The parameter \(a\)  is
nothing but a fraction in the expansion (REF ) divided by
\(\sqrt{}\) . Obviously, we are not dealing with a real solid: the
oscillations are damped, and the area under the curve, which
determines the self-diffusion coefficient, differs from zero [it
also follows from the inequality \(\tilde{F}_2(0)\ne 0\) , see
equation (REF )].
